At 5 p.m. on January 7, Marek Czarnecki (Warsaw University) will give a talk at the Centre for Logic and Philosophy of Science (room 2.30). If you're around, feel free to drop by.
We base on the notion of FM-representability introduced by M. Mostowski as an explication of representability without actual infinity. By Mostowski’s FM-representability theorem and Shoenfield’s Limit Lemma FM-representable notions are exactly those which uniformly computable limits of computable notions i.e. which are constructible in finitistic sense (by true constructions, not constructions relative to some uncomputable oracle).We introduce the notion of concrete models - FM-representable models - and consider the feasibility of classical model-theoretic constructions in concrete models framework. The aim is to identify the finitistic content of model theory - the part that has a computational meaning.More philosophically - studying concrete models provides with a better understanding of mathematical structures that are cognitively accessible and can be algorithmically learned. They can also be used for representing epistemologically feasible approximated representations of reality and cognitively accessible semantics.